This exercise shows that in a simple regression model, adding a dummy variable for missing data on the explanatory variable produces a consistent estimator of the slope coefficient if the “missingness”

is unrelated to both the unobservable and observable factors affecting y. Let m be a variable such that m 5 1 if we do not observe x and m 5 0 if we observe x. We assume that y is always observed. The population model is y 5 b0 1 b1x 1 u E1u0x2 5 0.

(i) Provide an interpretation of the stronger assumption E1u0x,m2 5 0.

In particular, what kind of missing data schemes would cause this assumption to fail?